An improved spectral turning-bands algorithm for simulating stationary vector Gaussian random fields

Emery, Xavier; Arroyo, Daisy; Porcu, Emilio

doi:10.1007/s00477-015-1151-0

Cited by 64 publications

(19 citation statements)

References 34 publications

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“…The Gaussian random fields are jointly simulated using a spectral turning-bands algorithm [36]. This algorithm is preferred to other alternatives, such as sequential, covariance matrix decomposition or circulant-embedding algorithms ( [26] and references therein) because of its accuracy, versatility, unequalled computational speeds, and low memory storage requirements, being able to simulate highly-multivariate random fields and to reproduce exactly the desired spatial correlation structure [36].…”

Section: Conditional Simulationmentioning

confidence: 99%

Geological Modelling and Validation of Geological Interpretations via Simulation and Classification of Quantitative Covariates

2017

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This paper proposes a geostatistical approach for geological modelling and for validating an interpreted geological model, by identifying the areas of an ore deposit with a high probability of being misinterpreted, based on quantitative coregionalised covariates correlated with the geological categories. This proposal is presented through a case study of an iron ore deposit at a stage where the only available data are from exploration drill holes. This study consists of jointly simulating the quantitative covariates with no previous geological domaining. A change of variables is used to account for stoichiometric closure, followed by projection pursuit multivariate transformation, multivariate Gaussian simulation, and conditioning to the drill hole data. Subsequently, a decision tree classification algorithm is used to convert the simulated values into a geological category for each target block and realisation. The determination of the prior (ignoring drill hole data) and posterior (conditioned to drill hole data) probabilities of categories provides a means of identifying the blocks for which the interpreted category disagrees with the simulated quantitative covariates.

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Section: Conditional Simulationmentioning

confidence: 99%

Geological Modelling and Validation of Geological Interpretations via Simulation and Classification of Quantitative Covariates

2017

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“…To get EZ o ≡ it is sufficient to assume E 0 Y ≡ . b) Recently, an improved spectral turning-bands algorithm for simulating stationary multivariate Gaussian random fields was presented in [3]. Using this one can simulate any multivariate Gaussian field whose cross-covariance function is continuous and absolutely integrable for each entry.…”

Section: Previous Simulation Approachesmentioning

confidence: 99%

“…Recently, a very interesting ansatz without this limitation was given in [3]. Similar to a kind of spectral turning-bands algorithm it is available for non-grid positions but it creates only approximately Gaussian fields.…”

Section: Introductionmentioning

confidence: 99%

Efficient Simulation of Stationary Multivariate Gaussian Random Fields with Given Cross-Covariance

Teichmann¹,

Boogaart²

2016

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The present paper introduces a new approach to simulate any stationary multivariate Gaussian random field whose cross-covariances are predefined continuous and integrable functions. Such a field is given by convolution of a vector of univariate random fields and a functional matrix which is derived by Cholesky decomposition of the Fourier transform of the predefined cross-covariance matrix. In contrast to common methods, no restrictive model for the cross-covariance is needed. It is stationary and can also be reduced to the isotropic case. The computational effort is very low since fast Fourier transform can be used for simulation. As will be shown the algorithm is computationally faster than a recently published spectral turning bands model. The applicability is demonstrated using a common numerical example with varied spatial correlation structure. The model was developed to support simulation algorithms for mineral microstructures in geoscience.

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“…The Cholesky decomposition is not suitable for samples with a larger number of locations, not least because the computing time of the algorithm is cubic in the number of variables. For functions possessing spectral densities with closed formulae, the spectral turning bands algorithm can be used (Arroyo and Emery (), Emery et al ()). The multivariate turning bands method is implemented in the R package RandomFields (Schlather et al ).…”

Section: Introductionmentioning

confidence: 99%

Fast and exact simulation of univariate and bivariate Gaussian random fields

Moreva

Schlather

2018

Stat

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Circulant embedding is a powerful algorithm for fast simulation of stationary Gaussian random fields on a rectangular grid in R n , which works perfectly for compactly supported covariance functions. Cut-off circulant embedding techniques have been developed for univariate random fields for dimensions up to R 3 and rely on the modification of a covariance function outside the simulation window, such that the modified covariance function is compactly supported. In this paper, we propose extensions of the cut-off approach for univariate and bivariate Gaussian random fields. In particular, we provide a method for simulating bivariate fields with a powered exponential model and the Matérn model for certain sets of parameters. Movie 2. Simulations from the bivariate Matérn model [To ensure that the visuanimation will play properly, use Adobe Acrobat Reader to view the pdf file.].holds. The covariance function C is stationary and isotropic if additionally C.h 1 / D C.h 2 / whenever kh 1 k D kh 2 k; that is, marginal covariances and cross-covariances depend only on the distance between the locations. Hereinafter, we write C.r/ instead of C.h/ with r D khk, whenever C.h/ is stationary and isotropic.where W is the one-dimensional discrete Fourier transform matrix of size 2N 2N with entries w pq D e 2 ipq=2N , p, q D 0, : : : , 2N 1, and W is the conjugate transpose of W. The eigenvalues in the diagonal matrix ƒ form the Figure 1. Toeplitz matrix and its circulant embedding matrix.

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An improved spectral turning-bands algorithm for simulating stationary vector Gaussian random fields

Cited by 64 publications

References 34 publications

Geological Modelling and Validation of Geological Interpretations via Simulation and Classification of Quantitative Covariates

Geological Modelling and Validation of Geological Interpretations via Simulation and Classification of Quantitative Covariates

Efficient Simulation of Stationary Multivariate Gaussian Random Fields with Given Cross-Covariance

Fast and exact simulation of univariate and bivariate Gaussian random fields

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